CAT 2021 Question Paper | Quant Slot 3

CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 15 : A shop owner bought a total of 64 shirts from a wholesale market that came in two sizes, small and large. The price of a small shirt was INR 50 less than that of a large shirt. She paid a total of INR 5000 for the large shirts, and a total of INR 1800 for the small shirts. Then, the price of a large shirt and a small shirt together, in INR, is

Video Explanation

Explanatory Answer

Let the number of small shirts be ‘x’
then the number of large shirts becomes 64 - x.
Let the price of a small shirt be ‘y’
then the price of a large shirt becomes y + 50
Money spent on small shirts = xy = 1800
Money spent on large shirts = (64 - x) (y + 50) = 5000
(64 - x) (y + 50) = 5000
64y + 3200 - xy - 50x = 5000
64y + 3200 - 1800 - 50x = 5000
64y + 1400 - 50x = 5000
64y - 50x = 3600
32y - 25x = 1800
32y - 25(1800/y) = 1800
32y² - 1800y - 25(1800) = 0
4y² - 9(25)y - 25(9)(25) = 0
y = 75
Price of a small shirt = ‘y’ = 75
Price of a small shirt = ‘y + 50’ = 125
The price of a large shirt and a small shirt together, in INR = 75 + 125 = 200

The answer is '200'

Choice D is the correct answer.

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